Desktop X refers to a desktop environment that uses the X Window System, which is the primary windowing system used by most Linux distributions. When someone says Desktop X, he's usually referring to the major desktop environments in the Linux ecosystem such as Gnome, KDE, ect.

So for example, this forum is named Desktop X, which means that this forum is for discussing problems you may have with the desktop environment itself. Problems like that involve something like unmovable windows, usability problems, missing taskbars, ect.

I'm pretty sure Desktop X has to do something with Windows and it's desktop. You may want to do some further research if you are looking into getting it soon. It seems pretty cool, and I may try it out myself.

DesktopX is a revolutionary software that allows you to change the desktop, and improve it with new items such as calendars, weather, stock quotes ...
DesktopX objects can be combined to create a fully customized desktop.

DesktopX is the tradename of a set of programs used in Windows. Since we are talking about Linux here, I think you are referring to X Desktop which is derived from X Window Manager.

X Desktop comes in many flavors which are independent of the distros. The default desktop usually is Gnome. Then there is a heavyweight desktop called KDE. On the other side of the scale, we have very minimalist desktops like Blackbox. Still on the light side and gaining popularity are LXDE and XFCE. XFCE is a bit ahead of LXDE after it's adopted by many distros like Linux Mint and Ubuntu.

Desktop X is a desktop enhancement program that allows users to build their own custom desktops. User creations can be exported as .desktop files or as widgets. The program is distributed with Object Desktop as well as stand-alone.
DesktopX is a program that lets users build their own desktops. These objects can come in all sizes and shapes. They can have scripts attached to them, they can be combined together to form mini applications or turned into an entire desktop.

Desktop X is a GUI(graphical user interface). It is what you move your mouse around in etc. You can open windows, use graphical word processors and much much more. This is different from a CLI(command line interface), where all you have is a prompt and a blinking cursor. You can only navigate a CLI with the keyboard, mice aren't supported. (A prompt is line of text that lets you know that the CLI is ready to take imput.)